/*
 * Copyright 2007 ZXing authors
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package fi.jasoft.qrcode.zxing;

/**
 * <p>
 * This class contains utility methods for performing mathematical operations
 * over the Galois Field GF(256). Operations use a given primitive polynomial in
 * calculations.
 * </p>
 * 
 * <p>
 * Throughout this package, elements of GF(256) are represented as an
 * <code>int</code> for convenience and speed (but at the cost of memory). Only
 * the bottom 8 bits are really used.
 * </p>
 * 
 * @author Sean Owen
 */
public final class GF256 {

    public static final GF256 QR_CODE_FIELD = new GF256(0x011D); // x^8 + x^4 +
                                                                 // x^3 + x^2 +
                                                                 // 1
    public static final GF256 DATA_MATRIX_FIELD = new GF256(0x012D); // x^8 +
                                                                     // x^5 +
                                                                     // x^3 +
                                                                     // x^2 + 1

    private final int[] expTable;
    private final int[] logTable;
    private final GF256Poly zero;
    private final GF256Poly one;

    /**
     * Create a representation of GF(256) using the given primitive polynomial.
     * 
     * @param primitive
     *            irreducible polynomial whose coefficients are represented by
     *            the bits of an int, where the least-significant bit represents
     *            the constant coefficient
     */
    private GF256(int primitive) {
        expTable = new int[256];
        logTable = new int[256];
        int x = 1;
        for (int i = 0; i < 256; i++) {
            expTable[i] = x;
            x <<= 1; // x = x * 2; we're assuming the generator alpha is 2
            if (x >= 0x100) {
                x ^= primitive;
            }
        }
        for (int i = 0; i < 255; i++) {
            logTable[expTable[i]] = i;
        }
        // logTable[0] == 0 but this should never be used
        zero = new GF256Poly(this, new int[] { 0 });
        one = new GF256Poly(this, new int[] { 1 });
    }

    GF256Poly getZero() {
        return zero;
    }

    GF256Poly getOne() {
        return one;
    }

    /**
     * @return the monomial representing coefficient * x^degree
     */
    GF256Poly buildMonomial(int degree, int coefficient) {
        if (degree < 0) {
            throw new IllegalArgumentException();
        }
        if (coefficient == 0) {
            return zero;
        }
        int[] coefficients = new int[degree + 1];
        coefficients[0] = coefficient;
        return new GF256Poly(this, coefficients);
    }

    /**
     * Implements both addition and subtraction -- they are the same in GF(256).
     * 
     * @return sum/difference of a and b
     */
    static int addOrSubtract(int a, int b) {
        return a ^ b;
    }

    /**
     * @return 2 to the power of a in GF(256)
     */
    int exp(int a) {
        return expTable[a];
    }

    /**
     * @return base 2 log of a in GF(256)
     */
    int log(int a) {
        if (a == 0) {
            throw new IllegalArgumentException();
        }
        return logTable[a];
    }

    /**
     * @return multiplicative inverse of a
     */
    int inverse(int a) {
        if (a == 0) {
            throw new ArithmeticException();
        }
        return expTable[255 - logTable[a]];
    }

    /**
     * @param a
     * @param b
     * @return product of a and b in GF(256)
     */
    int multiply(int a, int b) {
        if (a == 0 || b == 0) {
            return 0;
        }
        int logSum = logTable[a] + logTable[b];
        // index is a sped-up alternative to logSum % 255 since sum
        // is in [0,510]. Thanks to jmsachs for the idea
        return expTable[(logSum & 0xFF) + (logSum >>> 8)];
    }

}
